Fast Radio Bursts (FRBs) are short lived ($sim$ msec), energetic transients (having a peak flux density of $sim$ Jy) with no known prompt emission in other energy bands. We present results of a search for prompt X-ray emissions from 41 FRBs using the Cadmium Zinc Telluride Imager (CZTI) on AstroSat which continuously monitors $sim70%$ of the sky. Our searches on various timescales in the 20-200 keV range, did not yield any counterparts in this hard X-ray band. We calculate upper limits on hard X-ray flux, in the same energy range and convert them to upper bounds for $eta$: the ratio X-ray to radio fluence of FRBs. We find $eta leq 10^{8-10}$ for hard X-ray emission. Our results will help constrain the theoretical models of FRBs as the models become more quantitative and nearer, brighter FRBs are discovered.
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